jsfisher
ETcorngods survivor
- Joined
- Dec 23, 2005
- Messages
- 24,532
Sorta blows that whole thing about the orbit sphere being constant and uniform to pieces, no?
If you have access to the GUTCP book, the derivation leading up to Fig 1.21 shows how the convolution of the two current vector fields (CVF) Mills uses to create the orbitsphere leads to a constant uniform charge density.
That's still a loser right out of the gate. Mills' Big Book of Boo-Boos blunders quite early by failing to meet the Lorentz-invariant requirement for his charge-density function. (And I am confident you already know the reference.)
That aside, though, and against my better judgement, I did have a peek at the BBoBB. Is it of no concern whatsoever that resorting to not just one but two great circles of charge may be getting a bit arbitrary and that the choice for the axis for rotation for the two, orthogonal great circles is a bit arbitrary. (There may be an actual basis in Physics of all that, but it seems arbitrary to me.) But the thing of most concern, at least to this non-physicist, is that construction does not cover the entire sphere.
So, yeah, there seems to be a discrepancy.
Moreover, since I can construct your geodesic structure relative to any local coordinate system of my choosing, the direction of the Z-axis is arbitrary.
We know the electron has a z-axis from the results of the Stern-Gerlach experiment, which shows that the electron will only align up or down in a magnetic field.
So, the direction of the Z-axis is arbitrary in the absence of a magnetic field?
Moreover, moreover, for each of the "great circles", wouldn't the Z-axis be normal to the plane of circle? That would put all of them in the plane of the equator. Wouldn't those vectors all sum to zero?
Again, the derivation prior to Fig 1.21 shows how the two CVFs result in angular momentum vector components of L_z = 0.5 h_bar and L_xv = +/- 0.25 h_bar.
Apparently, since I was thinking you really needed to create a sphere as the surface of revolution, I took an entirely different approach than you (or Mills). However, I "over rotated" as it turns out; I went 360 degrees when I should have stopped at 180. The sum (whatever it might be) need not necessarily be zero.